In the city’s Greenwich neighborhood, a castle built around 1720 by Sir John Vanbrugh, a famous Georgian-era architect and playwright, is on the market

Britain is a land of castles, but aside from the famous Beefeaters who guard the Tower of London, almost nobody in London can claim to live in one—except for Dave and Barbara Edgar.

Their home for the past 20 years has been Vanbrugh Castle, a fortresslike folly built around 1720 by Sir John Vanbrugh, a great Georgian-era architect and playwright. He is said to have modeled his south London mansion on the French Bastille, where he was imprisoned on charges of spying for the British government.

When Mr. Edgar, now 60, and his wife, 59, first saw the castle, “it was a real rush of blood to the head moment,” said Mr. Edgar, who runs a branding and marketing company with his wife. “We just fell in love. And given its historic importance we also felt that we could be custodians of the castle for future generations.”

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Experts consider Vanbrugh Castle, located in Greenwich, one of the finest surviving buildings of its period. In 1719, 55-year-old Vanbrugh married 26-year-old Henrietta Yarburgh and designed their nuptial home. The British are known for their love of eccentricity, and Vanbrugh Castle is certainly quirky. This Gothic-style mansion includes defense towers, battlements and a central tower with a conical, copper roof.

“I think that Vanbrugh must have been a little paranoid, because when we moved in we discovered he had dug all sorts of quite spooky escape tunnels running from our cellar and out into the grounds,” said Mr.Edgar. “Because we had an inquisitive 8-year-old at the time, we also got a little bit paranoid and had them bricked up, but there are tunnels in the grounds which still exist.”

Sadly, Vanbrugh didn’t get to enjoy his castle for long.

He died after suffering an asthma attack in 1726, leaving Henrietta a widow with a young son, Charles.

In the years after Vanbrugh’s death the castle was sold. Subsequent residents included a novelist, an engineer who pioneered treatments for spinal injuries, and an oil merchant who donated it to the Royal Air Force to be used as a school for the children of officers killed in service.

It then fell into disrepair until, in 1976, a local conservation charity, the Blackheath Preservation Trust, took it on and converted it into four separate homes.

The Edgars own the central section of the castle, which measures just over 2,500 square feet. Laid out over three main floors it has four bedrooms and two bathrooms, as well as a cellar. Their favorite part of the home is its roof terrace, located in one of the battlement towers. “We have not met anyone who has not been gobsmacked by the views,” said Mr. Edgar.

Set on 2½ acres, the mansion has outdoor spaces that include gardens and woodland shared with the castle’s other homeowners. After they moved in, the Edgar family noticed the remains of a private amphitheater built by Vanbrugh for the purpose of putting on al fresco performances.

The property was in a “terrible state” when they bought it for £400,000, or about $585,000, in the mid-1990s. Before they could move in, they embarked on a yearlong restoration, upgrading aging plumbing and wiring, redecorating and installing a new kitchen and bathrooms.

Vanbrugh Castle is a heritage building, and it has the highest possible conservation status offered in the U.K.: Grade I Listed. This meant that significant changes to the property would be unlikely to be allowed.

As well as the cellar of their main house, the Edgars also own a second cellar, accessed via the backyard. They use this 600-square-foot space as a party room and for guest accommodation and storage.

The Edgars are now selling the castle because their son, Tom, is now 28 and has left home. So the couple wants to downsize and would like a more lock-up-and-leave home so they can travel more.

The castle is listed for £2.9 million, or about $4.2 million, and selling agent Christopher Venter, sales manager at Foxtons estate agents, believes the main interest is going to come from young couples, currently living in warehouse apartments in fashionable east London but who want to move further into the suburbs.

“They will be at the stage of life when they are thinking about things like good schools and open space, but they still want a home with the wow factor,” he explained.

The Edgar family is viewing its move with somewhat mixed feelings. “We all agree it is absolutely the right thing to do, but we are deliberately not talking about it,” said Mr. Edgar. “It is such an emotional subject. Moving day is going to be hard.”